Question

prove that Sin 780Sin 120° + Cos 240Sin390°= 1/2
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Answer 1

Answer:

)sin780.sin120+cos240.sin390

=sin(8x90+60).sin(90+30) +cos(3x90-30).sin(4x90+30)

=sin60.cos30+[-sin30].sin30

=sin60.cos30 - sin30.sin30

=(root3)/2 x (root3)/2 -1/2 x1/2

=3/4 -1/4

=2/4

=1/2(proved)

2)sin600.cos390 + cos 480.sin150

=sin(6x90+60).cos(4x90+30) + cos(5x90+30)sin(90+60)

=(-sin60).cos30 +-sin30.cos60

= -root3/2 x root3/2 +(-1/2 x 1/2)

= -3/4-1/4

=-1(proved)